http://sites.science.oregonstate.edu/portfolioswiki/ 2020-01-27T00:46:02-08:00 http://sites.science.oregonstate.edu/portfolioswiki/ http://sites.science.oregonstate.edu/portfolioswiki/lib/images/favicon.ico text/html 2012-08-23T22:24:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:index?rev=1345785846 text/html 2015-06-26T15:58:11-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvsw2nd?rev=1435359491 Prompt “Tell me something you know about the second-derivative test.” Context This SWBQ probes students' notions about optimization in single-variable calculus. Wrap Up text/html 2015-10-08T17:20:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswchain2?rev=1444350038 Prompt Suppose $T=2x+3y$ and $y=x+u$. Find $\frac{\partial T}{\partial x}$. Context This SWBQ ... Wrap Up text/html 2015-10-08T17:17:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswcircle?rev=1444349820 Prompt “Write down an integral for the area of a circle of radius 2.” Context This SWBQ introduces the use of curvilinear coordinates. Wrap Up Discuss different ways of chopping up the interior of a circle, such as: text/html 2015-06-26T15:57:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswdiff?rev=1435359458 Prompt “What is $dT\over dx$?” Context This SWBQ probes students' understanding of (ordinary) derivatives. Wrap Up text/html 2015-06-26T15:57:13-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswdiffex?rev=1435359433 Prompt “Differentiate $x^2$. Then differentiate $y^2$. Then $a^2$. Then $e^2$.” Context This SWBQ can be implemented to test students' understanding of differentiation. When students differentiate a function, they do not usually ask ``with respect to what.'' This SWBQ is intended to confront students with the idea that when differentiating a function they first need to think about this question. This SWBQ also provides an opportunity for the instructor to find out what the st… text/html 2015-06-26T15:57:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswdot?rev=1435359447 Prompt “Tell me something you know about the dot product.” Context This SWBQ probes students' notions about the dot product. Wrap Up text/html 2015-10-08T17:28:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswdrule?rev=1444350514 Prompt State a derivative rule. Context This SWBQ is designed to help students remember the derivative rules learned in single-variable calculus. Wrap Up We encourage the use of differentials to summarize the derivative rules, providing a coherent approach to both derivative and integration rules, as well as emphasizing “with respect to what”. Further discussion, along with a list of derivative rules in differential form can be found here. text/html 2015-06-26T15:56:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswintegrate?rev=1435359394 Prompt “What are integrals?” Context This SWBQ probes students' understanding of integration. Wrap Up text/html 2015-06-26T15:56:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswlim?rev=1435359387 Prompt “Is the integral (A) postive (B) negative or (C) zero?” [Original Powerpoint slide] [Original PDF slide] [Simplified PDF slide] Context This SWBQ emphasizes the geometry of integration, without (or prior to) computation. Wrap Up The original question is taken from the the ConcepTests book that accompanies Calculus, 4th edition, by Hughes Hallett et al, (cc) 2005 by John Wiley & Sons, Inc, and is used by permission. text/html 2015-10-08T18:39:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswmatch?rev=1444354768 Prompt “Match the region to the limits.” [Powerpoint slide] [PDF slide] Context This SWBQ probes students' understanding of the limits on double integrals. This SWBQ makes an excellent followup to one or both of the Triangle and Double Integral activities. text/html 2015-06-26T15:55:39-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswmaxmin?rev=1435359339 Prompt “Tell me something you know about finding maxima and minima.” Context This SWBQ probes students' notions about optimization in single-variable calculus. Wrap Up text/html 2016-09-23T11:24:10-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswpizza?rev=1474655050 Prompt “Which of the graphs below...” [PDF slides] Context This SWBQ provides an easy introduction to the graphical representation of functions of several variables. Wrap Up In each case, a brief discussion consists of asking for a student volunteer to describe how the shape of each graph is related to the corresponding prompt. Common answers typically analyze where the graphs are increasing or decreasing separately in the pizza and cola directions. text/html 2016-09-23T11:27:53-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswsurface?rev=1474655273 Prompt “How many ways can you represent a function of several variables?” Simpler prompts such as “What is a surface?” are not as effective because they lead students to use non-mathematical language. Context This SWBQ probes students' notions about surfaces. text/html 2015-06-26T15:55:08-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:mvswvec?rev=1435359308 Prompt “Tell me something you know about vectors.” Context This SWBQ probes students' notions about vectors. Wrap Up text/html 2015-06-26T15:52:20-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:mvsw:title?rev=1435359140 Multivariable Calculus SWBQs